投资组合前沿不适用于大型数据集

Question

我有一个自 2012 年以来的股票回报时间序列对象。portfolioFrontier 函数可以很好地创建我的效率边界，直到我将数据集扩展到月数之外。例如，我正在查看 39 个月，38 只股票一切正常。但是，一旦我添加了第 39 支股票（和第 40 支等），就会出现错误。代码和错误如下。

输入：

returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275, 
0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251, 
0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002, 
0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117, 
0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162, 
0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136, 
0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039, 
0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044, 
0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132, 
0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("Stock.A", "Stock.B", 
"Stock.C", "Stock.D", "Stock.E", "Stock.F", "Stock.G", "Stock.H", 
"Stock.I", "Stock.J")))
    , units = c("Stock.A", "Stock.B", "Stock.C", "Stock.D", "Stock.E",     "Stock.F", 
"Stock.G", "Stock.H", "Stock.I", "Stock.J")
    , positions = c(1327968000, 1330473600, 1333152000, 1335744000,     1338422400, 
1341014400, 1343692800, 1346371200)
    , format = "%Y-%m-%d"
    , FinCenter = "GMT"
    , recordIDs = structure(list(), .Names = character(0), row.names =     integer(0), class = "data.frame")
    , title = "Time Series Object"
        , documentation = "Tue Jun 23 13:48:36 2015"
    )

代码：

library(timeSeries)
library(fPortfolio)
# returns <- read.csv("Not Working Excel File.csv")
#lct <- Sys.getlocale("LC_TIME"); Sys.setlocale("LC_TIME", "C")
#returns[,1] = as.Date(as.character(returns[,1]),format="%d-%b-%y") 
#Sys.setlocale("LC_TIME", lct)
#returns = timeSeries(returns[,-1], charvec = returns[,1])
Frontier <- portfolioFrontier(returns)

错误：

Error in `colnames<-`(`*tmp*`, value = c("AAPL",  : 
  attempt to set 'colnames' on an object with less than two dimensions

如何解决此问题，以便在不添加日期的情况下添加我想要的股票数量？

编辑：这是数据集外观的快照。 http://i.imgur.com/i0hkBdY.png 因此，在这个包含 8 个月数据且只有四只股票的示例中，我在上面发布的代码运行良好。但是，一旦我再添加 5 只股票（总共 9 只），我就会得到上面列出的错误。

将数据框更改为矩阵会产生相同的错误。 添加更多月份可以让我添加更多股票，但我不想要更多月份。

Answer 1

问题

在不增加月（年）的情况下无法增加股票的原因似乎与最小化均值方差的问题有关。

来自 Cochrane“资产定价”第 81-83 页：

定理：只要收益的方差-协方差矩阵是非奇异的，就存在均值-方差边界。

问题“选择一个投资组合以最小化方差 对于给定的平均值”是

min{w} w0 Σw s.t. w0

您可以使用本书中概述的拉格朗日乘数方法来解决这个问题。然而，值得注意的是收益的协方差矩阵必须是非奇异的，这意味着协方差矩阵必须是正定的。如果您提供的用于计算边界的协方差矩阵是奇异的，则边界将不存在。

一个例子

输入：

returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275, 
    0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251, 
    0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002, 
    0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117, 
    0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162, 
    0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136, 
    0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039, 
    0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044, 
    0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132, 
    0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
    ), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("StockA", "StockB", 
    "StockC", "StockD", "StockE", "StockF", "StockG", "StockH", 
    "StockI", "StockJ")))
        , units = c("StockA", "StockB", "StockC", "StockD", "StockE", "StockF", 
    "StockG", "StockH", "StockI", "StockJ")
        , positions = c(1327968000, 1330473600, 1333152000, 1335744000, 1338422400, 
    1341014400, 1343692800, 1346371200)
        , format = "%Y-%m-%d"
        , FinCenter = "GMT"
        , recordIDs = structure(list(), .Names = character(0), row.names =     integer(0), class = "data.frame")
        , title = "Time Series Object"
            , documentation = "Tue Jun 23 13:48:36 2015"
        )

代码块 1：

# Load Matrix Checks 
library(matrixcalc)

# Get dimensions and check if positive definite
dim(returns)
is.positive.definite(cov(returns))

### Results ###
# > dim(returns)
#   [1]  8 10
# > is.positive.definite(cov(returns))
#   [1] FALSE

如您所见，协方差矩阵不是正定的，如果您尝试使用portfolioFrontier()，它将引发错误。

> portfolioFrontier(returns)
Error in `colnames<-`(`*tmp*`, value = c("StockA", "StockB", "StockC",  : 
  attempt to set 'colnames' on an object with less than two dimensions

代码块 2：

# Remove first three columns to fit n (obs) > m (stocks)
returns <- returns[,4:10]
dim(returns)

#Check if positive definite
is.positive.definite(cov(returns))

### Results ###
# > dim(returns)
# [1] 8 7
# > is.positive.definite(cov(returns))
# [1] TRUE

现在查看portfolioFrontier()

输出：

Title:
 MV Portfolio Frontier 
 Estimator:         covEstimator 
 Solver:            solveRquadprog 
 Optimize:          minRisk 
 Constraints:       LongOnly 
 Portfolio Points:  5 of 50 

Portfolio Weights:
   StockD StockE StockF StockG StockH StockI StockJ
1  0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
13 0.0000 0.0000 0.0000 0.1452 0.5016 0.2566 0.0966
25 0.0000 0.0000 0.0000 0.0000 0.1345 0.6738 0.1917
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.4758 0.5242
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

Covariance Risk Budgets:
    StockD  StockE  StockF  StockG  StockH  StockI  StockJ
1   0.0000  0.0000  0.0000  0.0000  1.0000  0.0000  0.0000
13  0.0000  0.0000  0.0000  0.1417 -0.0570  0.4871  0.4282
25  0.0000  0.0000  0.0000  0.0000 -0.0455  0.5865  0.4589
37  0.0000  0.0000  0.0000  0.0000  0.0000  0.2196  0.7804
50  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  1.0000

Target Returns and Risks:
     mean    Cov   CVaR    VaR
1  0.0001 0.0056 0.0080 0.0080
13 0.0048 0.0037 0.0025 0.0025
25 0.0094 0.0092 0.0122 0.0122
37 0.0141 0.0158 0.0238 0.0238
50 0.0191 0.0237 0.0370 0.0370

现在似乎可以工作了。因此，让我们绘制有效边界：

portfolio <- portfolioFrontier(returns)
plot(portfolio)